Low par zero auto-correlation zone sequences for code sequence modulation

ABSTRACT

In one non-limiting exemplary embodiment, a method includes: randomly selecting a set of sequences with each sequence having sequence elements, each sequence element having a frequency selected from constellation points on a unit circle in a complex plane, where the selected set of sequences is a candidate set of sequences; calculating a first cubic metric for each sequence of the candidate set of sequences, where the first cubic metric is for single code modulation; and in response to the first cubic metric being larger than at least one threshold, removing the corresponding sequence from the candidate set of sequences to obtain at least one saved sequence.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent application claims priority under 35 U.S.C. §119(e) fromU.S. Provisional Patent Application No. 60/936,379, filed Jun. 20, 2007,and from U.S. Provisional Patent Application No. 60/967,792, filed Sep.7, 2007, the disclosures of which are incorporated by reference hereinin their entirety.

TECHNICAL FIELD

The exemplary and non-limiting embodiments of this invention relategenerally to wireless communication systems, methods, devices andcomputer program products and, more specifically, relate to techniquesfor transmitting information between a user device and a wirelessnetwork device.

BACKGROUND

Certain abbreviations that may be found in the description and/or in theFigures are herewith defined as follows:

-   3GPP Third Generation Partnership Project-   CAZAC constant-amplitude zero auto-correlation-   CDF cumulative distribution function-   CDM code division multiplexing-   CDMA code division multiple access-   CM cubic metric-   CP cyclic prefix-   CQI channel quality indicator-   DFT discrete Fourier transform-   DFT-S-OFDM discrete Fourier transform spread OFDM (SC-FDMA based on    frequency domain processing)-   eNode B E-UTRAN Node B (eNB)-   E-UTRAN evolved UTRAN-   FDM frequency division multiplexing-   FDMA frequency division multiple access-   FFT fast Fourier transform-   IFFT inverse FFT-   LB long block-   LTE long term evolution of UTRAN (E-UTRAN)-   Node B base station-   OFDM orthogonal frequency division multiplexing-   OFDMA orthogonal frequency division multiple access-   PAR peak to average ratio-   PRB physical resource block-   PUCCH physical uplink control channel-   PUSCH physical uplink shared channel-   QPSK quadrature phase shift keying-   RAZAC random zero auto-correlation-   RRC radio resource control-   SC subcarrier-   SC-FDMA single carrier, frequency division multiple access-   SNR signal to noise ratio-   UE user equipment, such as a mobile station or mobile terminal-   UL uplink-   UTRAN universal terrestrial radio access network-   ZC Zadoff-Chu

A proposed communication system known as evolved UTRAN (E-UTRAN, alsoreferred to as UTRAN-LTE) is currently under discussion within the 3GPP.The working assumption is that the DL access technique will be OFDMA,and the UL technique will be SC-FDMA.

Reference may be made to Section 6 of 3GPP TR 36.211, V1.0.0 (2007-03),3rd Generation Partnership Project; Technical Specification Group RadioAccess Network; Physical Channels and Modulation (Release 8) for adescription of the UL physical channels.

Reference may also be made to 3GPP TR 25.814, V7.1.0 (2006-09), 3rdGeneration Partnership Project; Technical Specification Group RadioAccess Network; Physical layer aspects for evolved Universal TerrestrialRadio Access (UTRA) (Release 7), such as generally in section 9.1, for adescription of the SC-FDMA UL of E-UTRAN.

FIG. 1A reproduces FIG. 12 of 3GPP TS 36.211 and shows the UL slotformat for a generic frame structure.

As is described in Section 9.1 of 3GPP TR 25.814, the basic uplinktransmission scheme is single-carrier transmission (SC-FDMA) with cyclicprefix to achieve uplink inter-user orthogonality and to enableefficient frequency-domain equalization at the receiver side.Frequency-domain generation of the signal, sometimes known as DFT-spreadOFDM (DFT S-OFDM), is assumed.

FIG. 1B shows the generation of pilot samples. An extended or truncatedZadoff-Chu symbol sequence is applied to an IFFT block via a sub-carriermapping block. The sub-carrier mapping block determines which part ofthe spectrum is used for transmission by inserting a suitable number ofzeros at the upper and/or lower end. A CP is inserted into the output ofthe IFFT block.

In the PUCCH sub-frame structure for the UL control signaling, sevenSC-FDMA symbols (also referred to herein as “LBs” for convenience) arecurrently defined per slot. A sub-frame consists of two slots. Part ofthe LBs are used for reference signals (pilot long blocks) for coherentdemodulation. The remaining LBs are used for control and/or datatransmission.

The current working assumption is that for the PUCCH the multiplexingwithin a PRB is performed using CDM and (localized) FDM is used fordifferent resource blocks. In the PUCCH, the bandwidth of one controland pilot signal always corresponds to one PRB=12 SCs.

Two types of CDM are used both for data and pilot LBs. Multiplexingbased on the usage of cyclic shifts provides nearly completeorthogonality between different cyclic shifts if the length of cyclicshift is larger than the delay spread of the radio channel. For example,with an assumption of a 5 microsecond delay spread in the radio channel,up to 12 orthogonal cyclic shifts within one LB can be achieved.Sequence sets for different cells are obtained by changing the sequenceindex.

Another type of CDM may be applied between LBs based on orthogonalcovering sequences, e.g., Walsh or DFT spreading. This orthogonalcovering may be used separately for those LBs corresponding to the RSand those LBs corresponding to the data signal. The CQI is typicallytransmitted without orthogonal covering.

Of particular interest to the exemplary embodiments of this invention iscontrol channel signaling and, in particular, the use of the PUCCH.

As was noted, it has been determined in 3GPP that UEs having CQItransmission are code division multiplexed by means of different cyclicshifts of CAZAC sequences. In commonly owned and copending U.S.Provisional Patent Application No. 60/933,760, filed Jun. 8, 2007, byKari Pajukoski, Esa Tiirola and Kari Hooli, entitled: Multi-codePrecoding for CAZAC Sequence Modulation, Nokia Siemens Networks OyDocket No.: 2007P02633, Harrington & Smith, PC Docket No. 863.0066.P1(US), multi-code sequence modulation is provided to allow for larger CQIsizes, and a multi-code preceding for CAZAC sequence modulation isdescribed.

One problem related to conventional CAZAC sequence modulation is thesmall spectrum efficiency per UE, due to the fact that only onemodulated CAZAC sequence per UE can be transmitted during the longblock. Correspondingly, the maximum symbol rate is limited to one symbolper block. Spectrum efficiency can be increased by transmitting multiplemodulated CAZAC sequences simultaneously, however the use of thisapproach suffers from an increased PAR, which in turn results in eitherhigher UE power consumption or decreased CQI coverage. The precedingmethod disclosed in U.S. Provisional Patent Application No. 60/933,760significantly reduces PAR for multi-code sequence modulation. However,multi-code sequence modulation can still exhibit a larger PAR thansingle code sequence modulation.

3GPP has proposed the use of Zadoff-Chu sequences, as well as theextended and truncated modifications of Zadoff-Chu sequences, consideredtogether with numerically searched CAZAC-like sequences. However, themulti-code sequence modulation has not been considered in the design ofthese sequences and one result of this is an increase in CM whenmulti-code sequence modulation is applied.

In 3GPP TSG RAN WG1 #49, Kobe, Japan, May 7-11, 2007, “Design of CAZACSequences for Small RB Allocations in E-UTRA UL”, Texas Instruments,R1-072206, a numerical search method for CAZAC-like sequences ispresented. The method can be approximately summarized as follows:

-   1. A set of initial sequences are randomly selected with elements on    the unit circle.-   2. Sequences are iterated with two steps in a loop:    -   a. Sequences are forced to flat in frequency by dividing each        sequence element with its amplitude; and    -   b. Sequences are forced to flat in time by dividing each        sequence element with its amplitude.

More specifically, R1-072206 describes a method for generating CAZACsequences by computer search using random initialization. Because arandom procedure is used to search these CAZAC sequences, they arereferred to as Random-CAZAC. The procedure for generating the CAZACsequence of length N is as follows:

-   -   (1) Let i=1, in the first step generate N QPSK random complex        numbers:        {tilde over (X)} _(i) ^(f)={{tilde over (x)} _(i) ^(f)(1),        {tilde over (x)} _(i) ^(f)(2), . . . {tilde over (x)} _(i)        ^(f)(n) . . . , {tilde over (x)} _(i) ^(f)(N)}; {tilde over (x)}        _(i) ^(f)(n)ε{1+j, 1−j, −1+j, −1−j}.    -   (2) Next, define the sequence:

${X_{i}^{f} = {\left\{ {{x_{1}^{f}(1)},{x_{1}^{f}(2)},{\ldots\mspace{14mu}{x_{1}^{f}(n)}\mspace{14mu}\ldots}\mspace{14mu},{x_{1}^{f}(N)}} \right\} = {\left\{ {\frac{{\overset{\sim}{x}}_{i}^{f}(1)}{{{\overset{\sim}{x}}_{i}^{f}(1)}},\frac{{\overset{\sim}{x}}_{i}^{f}(2)}{{{\overset{\sim}{x}}_{i}^{f}(2)}},{\ldots\mspace{14mu}\frac{{\overset{\sim}{x}}_{i}^{f}(n)}{{{\overset{\sim}{x}}_{i}^{f}(n)}}\ldots}\mspace{14mu},\frac{{\overset{\sim}{x}}_{i}^{f}(N)}{{{\overset{\sim}{x}}_{i}^{f}(N)}}} \right\}.}}}\mspace{14mu}$

-   -   (3) Let sequence {tilde over (X)}_(i) ^(t)={{tilde over (x)}_(i)        ^(t)(1), {tilde over (x)}_(i) ^(t)(2), . . . , {tilde over        (x)}_(i) ^(t)(N)} be the IFFT of sequence {tilde over (X)}_(i)        ^(f), and define the sequence:

$X_{i}^{t} = {\left\{ {{x_{i}^{t}(1)},{x_{i}^{t}(2)},{\ldots\mspace{14mu}{x_{i}^{t}(n)}\mspace{14mu}\ldots}\mspace{14mu},{x_{i}^{t}(N)}} \right\} = {\left\{ {\left( \frac{{\overset{\sim}{x}}_{i}^{t}(1)}{{{\overset{\sim}{x}}_{i}^{t}(1)}} \right),\left( \frac{{\overset{\sim}{x}}_{i}^{t}(2)}{{{\overset{\sim}{x}}_{i}^{t}(2)}} \right),{\ldots\mspace{14mu}\left( \frac{{\overset{\sim}{x}}_{i}^{t}(n)}{{{\overset{\sim}{x}}_{i}^{t}(n)}} \right)\mspace{14mu}\ldots\mspace{14mu}\left( \frac{{\overset{\sim}{x}}_{i}^{t}(N)}{{{\overset{\sim}{x}}_{i}^{t}(N)}} \right)}} \right\}.}}$

-   -   (4) Let the FFT of the sequence X_(i) ^(t) be now denoted by        {tilde over (X)}_(i) ^(f); set i=i+1 and go back to step (2).        Repeat the above steps (2), (3) and (4) for say M=1000 or more.

For large number of iterations, it is said that it was found that theresulting sequence X_(M) ^(t) is a CAZAC sequence. Further, several suchCAZAC sequences can be generated by starting with a different randomsequence in step (1) above.

SUMMARY

The below summary section is intended to be merely exemplary andnon-limiting.

In one exemplary embodiment of the invention, a method comprising:randomly selecting a set of sequences with each sequence comprised ofsequence elements, each sequence element having a frequency selectedfrom constellation points on a unit circle in a complex plane, where theselected set of sequences comprises a candidate set of sequences;calculating a first cubic metric for each sequence of the candidate setof sequences, where the first cubic metric is for single codemodulation; and in response to the first cubic metric being larger thanat least one threshold, removing the corresponding sequence from thecandidate set of sequences to obtain at least one saved sequence.

In another exemplary embodiment of the invention, a program storagedevice readable by a machine, tangibly embodying a program ofinstructions executable by the machine for performing operations, saidoperations comprising: randomly selecting a set of sequences with eachsequence comprised of sequence elements, each sequence element having afrequency selected from constellation points on a unit circle in acomplex plane, where the selected set of sequences comprises a candidateset of sequences; calculating a first cubic metric for each sequence ofthe candidate set of sequences, where the first cubic metric is forsingle code modulation; and in response to the first cubic metric beinglarger than at least one threshold, removing the corresponding sequencefrom the candidate set of sequences to obtain at least one savedsequence.

In another exemplary embodiment of the invention, an apparatuscomprising: a memory and at least one processor, where the at least oneprocessor is configured to: randomly select a set of sequences with eachsequence comprised of sequence elements, each sequence element having afrequency selected from constellation points on a unit circle in acomplex plane, where the selected set of sequences comprises a candidateset of sequences; calculate a first cubic metric for each sequence ofthe candidate set of sequences, where the first cubic metric is forsingle code modulation; and in response to the first cubic metric beinglarger than at least one threshold, remove the corresponding sequencefrom the candidate set of sequences to obtain at least one savedsequence, where the at least one saved sequence is stored on the memory.

In another exemplary embodiment of the invention, an apparatuscomprising: means for randomly selecting a set of sequences with eachsequence comprised of sequence elements, each sequence element having afrequency selected from constellation points on a unit circle in acomplex plane, where the selected set of sequences comprises a candidateset of sequences; means for calculating a first cubic metric or eachsequence of the candidate set of sequences, where the first cubic metricis for single code modulation; and means, in response to the first cubicmetric being larger than at least one threshold, for removing thecorresponding sequence from the candidate set of sequences to obtain atleast one saved sequence.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other aspects of exemplary embodiments of thisinvention are made more evident in the following Detailed Description,when read in conjunction with the attached Drawing Figures, wherein:

FIG. 1A reproduces FIG. 12 of 3GPP TS 36.211 and shows the UL slotformat for a generic frame structure;

FIG. 1B is a block diagram that illustrates the generation of pilotsamples for the 3GPP LTE SC-FDMA UL;

FIG. 2 shows a simplified block diagram of various electronic devicesthat are suitable for use in practicing the exemplary embodiments ofthis invention;

FIG. 3 is a graph that presents the CDF of CM for extended and truncatedZadoff-Chu sequences, as well as for 12 exemplary RAZAC sequences, withresults for both single code (1×) and multi-code (2×) modulation beingdepicted;

FIG. 4 is a logic flow diagram in accordance with exemplary embodimentsof a method, and a computer program product, in accordance with thisinvention for determining the set of random zero auto-correlation(RAZAC) sequences shown in FIG. 5;

FIGS. 5A-5E, collectively referred to as FIG. 5, show a set of RAZACsequences in accordance with the exemplary embodiments of thisinvention;

FIGS. 6A and 6B, collectively referred to as FIG. 6, show a selectedsubset of the set of RAZAC sequences of FIG. 5;

FIG. 7 is a logic flow diagram in accordance with exemplary embodimentsof a method, and a computer program product, in accordance with thisinvention for use in selecting the subset of RAZAC sequences shown inFIG. 6;

FIG. 8 shows a set of RAZAC-like sequences for length 1RB PUSCHdemodulation reference sequences in accordance with the exemplaryembodiments of this invention;

FIGS. 9A-9C, collectively referred to as FIG. 9, show a set ofRAZAC-like sequences for length 2RB PUSCH demodulation referencesequences in accordance with the exemplary embodiments of thisinvention;

FIG. 10 is another logic flow diagram in accordance with exemplaryembodiments of a another method, and a computer program product, inaccordance with this invention for use in selecting a subset of theexemplary RAZAC-like sequences shown in FIG. 9;

FIG. 11 is another logic flow diagram in accordance with exemplaryembodiments of a another method, and a computer program product, inaccordance with this invention for use in selecting a set of theexemplary sequences;

FIG. 12 is another logic flow diagram in accordance with exemplaryembodiments of a another method, and a computer program product, inaccordance with this invention for use in selecting a set of theexemplary sequences; and

FIG. 13 is another logic flow diagram in accordance with exemplaryembodiments of a another method, and a computer program product, inaccordance with this invention for use in selecting a set of theexemplary sequences.

DETAILED DESCRIPTION

The exemplary embodiments of this invention pertain at least in part tothe UL portion of the LTE, and, more specifically, pertain to PUCCH DLCQI modulation in the UL PUCCH channel. The exemplary embodiments ofthis invention provide novel sequences suitable for both multi-code andsingle-code sequence modulation while exhibiting a low PAR. Theexemplary embodiments of this invention also provide novel sequencessuitable as PUSCH demodulation reference sequences, for example, forboth 1 and 2 resource block (RB) allocations.

By way of introduction, reference is made to FIG. 2 for illustrating asimplified block diagram of various electronic devices that are suitablefor use in practicing the exemplary embodiments of this invention. InFIG. 2, a wireless network 1 is adapted for communication with a UE 10via at least one Node B (base station) 12 (also referred to herein as aneNode B 12). The network 1 may include a network control element 14coupled to the eNode B 12 via a data path 13. The UE 10 includes a dataprocessor (DP) 10A, a memory (MEM) 10B that stores a program (PROG) 10C,and a suitable radio frequency (RF) transceiver 10D having a transmitter(T) and a receiver (R) for bidirectional wireless communication with theeNode B 12, which also includes a DP 12A, a MEM 12B that stores a PROG12C, and a suitable RF transceiver 12D having a transmitter (T) and areceiver (R). The eNode B 12 is typically coupled via the data path 13to the network control element 14 that also includes at least one DP 14Aand a MEM 14B storing an associated PROG 14C. At least one of the PROGs10C and 12C is assumed to include program instructions that, whenexecuted by the associated DP, enable the respective electronic deviceto operate in accordance with the exemplary embodiments of thisinvention, as will be discussed below in greater detail.

In a typical implementation, there will be a plurality of UEs 10 thatare present and that require the use of UL signaling.

In general, the various embodiments of the UE 10 can include, but arenot limited to, cellular telephones, personal digital assistants (PDAs)having wireless communication capabilities, portable computers havingwireless communication capabilities, image capture devices such asdigital cameras having wireless communication capabilities, gamingdevices having wireless communication capabilities, music storage andplayback appliances having wireless communication capabilities, Internetappliances permitting wireless Internet access and browsing, as well asportable units or terminals that incorporate combinations of suchfunctions.

The exemplary embodiments of this invention may be implemented bycomputer software executable by the DP 10A of the UE 10 and the DP 12Aof the eNode B 12, or by hardware, or by a combination of software (andfirmware) and hardware.

The MEMs 10B, 12B and 14B may be of any type suitable to the localtechnical environment and may be implemented using any suitable datastorage technology, such as semiconductor-based memory devices, flashmemory, magnetic memory devices and systems, optical memory devices andsystems, fixed memory and removable memory. The DPs 10A, 12A and 14A maybe of any type suitable to the local technical environment, and mayinclude one or more of general purpose computers, special purposecomputers, microprocessors, digital signal processors (DSPs) andprocessors based on a multi-core processor architecture, as non-limitingexamples.

Discussing now in greater detail the exemplary embodiments of thisinvention, there is provided a set of numerically searched sequenceswhich have the following properties:

-   -   nearly zero auto-correlation zone that provide nearly orthogonal        cyclic shifts and flat frequency response;    -   a CM mainly below 1 dB with single-code sequence modulation; and    -   a low CM when used with the precoded multi-code sequence        modulation presented in U.S. Provisional Patent Application No.        60/933,760.

The disclosed sequences may be differentiated from the sequencespreviously considered in 3GPP in at least two main respects. First, thesequences exhibit a low CM with precoded multi-code sequence modulation.Second, the sequences do not have constant amplitude in time, thus, theyare not characterized as CAZAC-like sequence. Instead, they may becharacterized generally as random zero auto-correlation (RAZAC)sequences or as RAZAC-like sequences.

An exemplary set of 53 RAZAC sequences is presented in FIGS. 5A-5E. Inthis case, each of the 53 sequences has 12 elements each comprised of avalue having a real and an imaginary part. In FIGS. 5A-5E, the sequencesare presented both in the frequency and time domains. From the set ofsequences, sequence subsets may be selected so that thecross-correlations between the sequences within the subset arereasonable (acceptable for use). A non-limiting example of such a subsetcontaining 12 sequences is shown in FIGS. 6A and 6B, and includes thesequences 4, 20, 21, 24, 26, 31, 32, 33, 36, 39, 46 and 51 from the setof RAZAC sequences shown in FIG. 5. Such a subset allows for a sequencereuse factor of 12.

It should be pointed out that FIG. 5 is not intended to present anexhaustive list of RAZAC sequences, and that there may be others thatcould be employed. It is also pointed out that the RAZAC sequences maybe rotated and/or scaled by multiplying the entire sequence by a complexnumber. However, this type of operation does not fundamentally changethe sequence.

The sequences may be numerically searched with the following method thatforms an aspect of the exemplary embodiments of this invention(reference is also made to FIG. 4 in this regards).

4A. A set of initial sequences are randomly selected with elements onthe unit circle.

4B. The sequences are iterated with three steps in a loop:

-   -   4Ba. Sequences are forced to flat in frequency by dividing each        sequence element with its amplitude.    -   4Bb. For each sequence, the CM is calculated for both single        code and multi-code modulation. If both CMs are less than some        given thresholds, and less than the CM during previous        iterations, the sequence is saved. This step may be performed        every n^(th) iteration (e.g., every 5^(th) iteration).    -   4Bc. For each sequence, the variance of the sequence element        amplitudes in time is calculated for both single code and        multi-code modulation. If the variance with single code        modulation is larger than with multi-code modulation, the        sequence with single code modulation is forced to flat in time        by dividing sequence elements with the amplitude. If the        variance with multi-code modulation is larger than with single        code modulation, the sequence with multi-code modulation is        forced to flat in time by dividing each sequence element with        its amplitude.

During the search, different exemplary embodiments of the method mayused with differences in steps 4Bb and 4Bc. Note that the presence andexecution of the steps 4Bb and 4Bc is clearly different than the searchmethod discussed above for R1-072206.

The unit circle may be a unit circle in the complex plane such that thefrequencies for the sequence elements of the randomly selected sequenceshave a real part and an imaginary part, as with the examples shown inFIGS. 5, 6, 8 and 9, as described in greater detail below. In someexemplary embodiments, each sequence element has a frequency selectedfrom constellation points on a unit circle (see FIGS. 8 and 9). In someexemplary embodiments, each sequence element has a frequency selectedfrom four constellation points on a unit circle (see FIGS. 8 and 9). Theconstellation points (e.g., the four constellation points) may beevenly-spaced about the unit circle (see FIGS. 8 and 9). In someexemplary embodiments, the constellation points comprise QPSKconstellation points.

From the obtained set of sequences, a subset may be selected from itwith the following method that also forms an aspect of the exemplaryembodiments of this invention (reference is made to FIG. 7 in thisregard).

7A. All sequences are included in a candidate sequence subset.Cross-correlations are calculated for all sequence pairs. For eachsequence pair, cross-correlations are calculated for all cyclic shiftcombinations, from which the cross-correlation value with the largestamplitude is selected as a cross-correlation representative value forthe cross-correlations between that sequence pair.

7B. Three cross-correlation thresholds C1, C2, C3 are selected so thatC1>C2>C3.

7C. Calculations are iterated in a loop so that one sequence is removedfrom the candidate subset on each iteration. Iterations are continueduntil there remain a desired number of sequences in the candidatesubset, or no sequences are found to be removed. There are four steps inthe loop:

-   -   7Ca. For each sequence, denoted with k, the related        cross-correlation representative values are examined. The number        of representative values exceeding a cross-correlation threshold        is counted for each threshold C1, C2, C3, resulting in A1(k),        A2(k), A3(k).    -   7Cb. Only the sequences having A1 equal to the maximum A1 value        over all sequences are selected for further consideration in        7Cc.    -   7Cc. Only the sequences having A2 equal to the maximum A2 value        over all sequences considered in 7Cc are selected for further        consideration in 7Cd.    -   7Cd. The sequence having the largest A3 value over all sequences        considered in 7Cd is removed from the candidate sequence subset.        If there are multiple sequences with the largest A3 value, one        sequence from those is selected to be removed. Also the        cross-correlation representative values related to the removed        sequence are removed from the calculation.

As non-limiting examples, the sequences as described above may be usedfor sequence modulation on the PUCCH, as well as for demodulation andsounding reference signals of length 12. When considering sequencemodulation on the PUCCH, a reasonable subset of sequences, such as inFIG. 6, may be defined and saved in the memories 10B, 12B of the UE 10and the eNB 12. Sequences and their cyclic shifts may be allocated bymeans of higher layer signaling (e.g., by RRC signaling). The sequenceindex may be cell-specific, whereas the cyclic shift index or indicesmay be resource-specific and/or UE-specific. The modulation used withmulti-code sequence modulation may be as described in U.S. ProvisionalPatent Application No. 60/933,760. In addition, the two cyclic shiftsused in the multi-code modulation may be consecutive, e.g., one of thepairs {0,1}, {2,3}, {4,5}, {6,7}, {8,9}, {10,11}.

In further exemplary embodiments of the invention, exemplary sets of 30RAZAC-like sequences of 1 and 2 RB lengths for PUSCH demodulationreference sequences are presented in FIGS. 8 and 9, respectively. Inthis case each of the 30 sequences has 12 elements (1 RB length) or 24elements (2 RB length) in frequency, each element comprised of a valuehaving a real and an imaginary part. These values are restricted so thatthey can be represented with 2 bits. This limits the number of allowedvalues per sequence element to 4. Due to this limited sequence set, acandidate sequence set can be searched with conventional numericalsearch methods so that the candidate sequence set fulfills the followingthree requirements:

-   -   Sequences have low PAR with single sequence modulation and with        multi-sequence modulation in the case of sequences of length 12.    -   Sequences have reasonable (i.e., acceptable for use)        cross-correlations with extended Zadoff-Chu sequences of length        36.    -   Sequences of length 24 have reasonable (i.e., acceptable for        use) cross-correlations with a set of sequences of length 12        (which is selected first).

However, to select a sequence set from the exemplary candidate sequenceset(s) so that the cross-correlations between the sequences within theset are reasonable (i.e., acceptable for use), the following variant ofthe method depicted in FIG. 7 may be used. This variant is shown in theexemplary logic flow diagram of FIG. 10.

10A. All sequences are included in a candidate sequence subset.Cross-correlations are calculated for all sequence pairs. For eachsequence pair, cross-correlations are calculated for all cyclic shiftcombinations, from which the cross-correlation value with the largestamplitude is selected as a cross-correlation representative value forthe cross-correlations between that sequence pair. In addition, for eachsequence pair, mean squared difference between cross-correlations andm/sqrt(N) is calculated over all cyclic shift combinations, resulting inB2(k). N is the sequence length and k is the sequence index. The value1/sqrt(N) is the cross-correlation value between Zadoff-Chu sequencesand m is a scaling factor.

10B. Cross-correlation threshold D and scaling factor m are selected.

10C. Calculations are iterated in a loop so that one sequence is removedfrom the candidate subset on each iteration. Iterations are continueduntil there remain a desired number of sequences in the candidatesubset, or no sequences are found to be removed. There are three stepsin the loop:

-   -   10Ca. For each sequence, denoted with k, the related        cross-correlation representative values are examined. The number        of representative values exceeding a cross-correlation threshold        C is counted for threshold D, resulting in B1(k).    -   10Cb. Only the sequences having B13 equal to the maximum B1        value over all sequences are selected for further consideration        in 10Cc.    -   10Cc The sequence with the largest mean squared difference B2(k)        is discarded.

It should be noted that threshold C may be adjusted and calculationrepeated to obtain a sequence set of a desired size. In addition, meancross-correlation between a sequence pair may be used instead of themean squared difference.

As further non-limiting examples, the sequence sets selected asdescribed above may be used for sequence modulation on the PUCCH, aswell as for demodulation and sounding reference signals of lengths 12and 24.

As should be appreciated, a number of advantages can be realized by theuse of the exemplary embodiments of this invention. For example, andreferring to FIG. 3, the CDF of the CM is presented for extended andtruncated Zadoff-Chu (ZC) sequences, as well as for the subset of 12RAZAC sequences shown in FIG. 6. It can be seen that for the RAZACsequences only few cyclic shifts of the sequences have a CM greater than1 dB in the case of single code modulation. In addition, the CM remainsless than 1 dB in the case of multi-code modulation. Thus, the RAZACsequences shown in FIGS. 5 and 6 provide a significant improvement inthe CM as compared to truncated and extended Zadoff-Chu sequences.Although not shown in FIG. 3, the sequences presented in R1-072206exhibit high CM values in the case of multi-code modulation withconsecutive cyclic shifts. One should also note that due at least to UE10 power limitations, differences in CM values that are less than 1 dBare generally not significant.

Based on the foregoing it should be apparent that the exemplaryembodiments of this invention provide for, in a non-limiting aspectthereof, a method, apparatus and computer program product for providinga user equipment with a plurality of RAZAC or RAZAC-like sequences foruse in single-code or multi-code sequence modulation of an uplinktransmission to a base station.

The exemplary embodiments of this invention further provide forprecoding the multi-code sequence modulation.

Further in accordance with exemplary embodiments of this invention, theUE 10 of FIG. 2 is constructed to contain circuitry (e.g., at least onememory) configured to store a plurality of RAZAC sequences for use insingle-code or multi-code sequence modulation of an uplink transmissionto a base station, where the UE may further include circuitry configuredto precode the multi-code sequence modulation.

Below are provided further descriptions of non-limiting, exemplaryembodiments. The below-described exemplary embodiments are separatelynumbered for clarity and identification. This numbering should not beconstrued as wholly separating the below descriptions since variousaspects of one or more exemplary embodiments may be practiced inconjunction with one or more other aspects or exemplary embodiments.

-   (1) In one non-limiting, exemplary embodiment, and as shown in FIG.    11, a method comprising: randomly selecting a set of sequences with    each sequence comprised of sequence elements, each sequence element    having a frequency selected from constellation points on a unit    circle in a complex plane, where the selected set of sequences    comprises a candidate set of sequences (801); calculating a first    cubic metric for each sequence of the candidate set of sequences,    where the first cubic metric is for single code modulation (802);    and in response to the first cubic metric being larger than at least    one threshold, removing the corresponding sequence from the    candidate set of sequences to obtain at least one saved sequence    (803).

A method as in any above, further comprising: calculating a second cubicmetric for each sequence of the candidate set of sequences, where thesecond cubic metric is for multi-code modulation; and in response to atleast one of the first cubic metric or the second cubic metric beinglarger than the at least one threshold, removing the correspondingsequence from the candidate set of sequences to obtain that at least onesaved sequence. A method as in any above, where the at least onethreshold comprises a first threshold and a second threshold, whereremoving the corresponding sequence is performed in response to at leastone of the first cubic metric being larger than the first threshold orthe second cubic metric being larger than the second threshold. A methodas in any above, further comprising: calculating cross-correlations fora plurality of different cyclic shift combinations of each sequence ofthe candidate set of sequences against a second sequence set; selectinga cross-correlation value having a largest amplitude as a representativecross-correlation value for the cross-correlations between thecorresponding sequence and the second sequence set; and in response tothe representative cross-correlation value being larger than athreshold, removing the corresponding sequence from the candidate set ofsequences. A method as in any above, where the second sequence set iscomprised of second sequences having a length of 36 sequence elements orsecond sequences having a length of 12 sequence elements. A method as inany above, where each sequence element of the sequences in the selectedset of sequences has a frequency selected from four possibleconstellation points on a unit circle in a complex plane. A method as inany above, where the at least one saved sequence has a length of oneresource block or two resource blocks.

A method as in any above, where the at least one saved sequencecomprises at least one of:

element 1  0.7071 − 0.7071i −0.7071 + 0.7071i  0.7071 + 0.7071i 0.7071 +0.7071i 2 −0.7071 + 0.7071i  0.7071 + 0.7071i  0.7071 + 0.7071i−0.7071 + 0.7071i  3  0.7071 − 0.7071i  0.7071 − 0.7071i −0.7071 −0.7071i 0.7071 + 0.7071i 4  0.7071 + 0.7071i  0.7071 − 0.7071i −0.7071 −0.7071i 0.7071 − 0.7071i 5 −0.7071 − 0.7071i −0.7071 + 0.7071i −0.7071 −0.7071i 0.7071 + 0.7071i 6 −0.7071 − 0.7071i −0.7071 + 0.7071i −0.7071 −0.7071i −0.7071 + 0.7071i  7 −0.7071 − 0.7071i −0.7071 − 0.7071i  0.7071− 0.7071i −0.7071 + 0.7071i  8 −0.7071 − 0.7071i  0.7071 + 0.7071i−0.7071 + 0.7071i −0.7071 + 0.7071i  9 −0.7071 − 0.7071i −0.7071 +0.7071i −0.7071 − 0.7071i 0.7071 − 0.7071i 10  0.7071 + 0.7071i 0.7071 + 0.7071i  0.7071 + 0.7071i 0.7071 − 0.7071i 11  0.7071 −0.7071i −0.7071 + 0.7071i −0.7071 − 0.7071i −0.7071 + 0.7071i  12−0.7071 − 0.7071i −0.7071 + 0.7071i −0.7071 + 0.7071i 0.7071 − 0.7071ielement 1 −0.7071 − 0.7071i  −0.7071 − 0.7071i  0.7071 + 0.7071i 2−0.7071 + 0.7071i   0.7071 + 0.7071i −0.7071 + 0.7071i 3 0.7071 +0.7071i  0.7071 + 0.7071i −0.7071 + 0.7071i 4 0.7071 + 0.7071i −0.7071 +0.7071i −0.7071 + 0.7071i 5 −0.7071 − 0.7071i  −0.7071 − 0.7071i  0.7071− 0.7071i 6 0.7071 + 0.7071i −0.7071 + 0.7071i  0.7071 − 0.7071i 7−0.7071 − 0.7071i  −0.7071 − 0.7071i −0.7071 − 0.7071i 8 −0.7071 −0.7071i  −0.7071 − 0.7071i −0.7071 − 0.7071i 9 0.7071 − 0.7071i−0.7071 + 0.7071i  0.7071 + 0.7071i 10 0.7071 − 0.7071i  0.7071 +0.7071i −0.7071 − 0.7071i 11 0.7071 + 0.7071i −0.7071 + 0.7071i−0.7071 + 0.7071i 12 −0.7071 − 0.7071i   0.7071 − 0.7071i  0.7071 −0.7071i

A method as in any above, where the at least one saved sequencecomprises at least one of:

element 1 −0.7071 − 0.7071i −0.7071 + 0.7071i  −0.7071 − 0.7071i 2−0.7071 − 0.7071i 0.7071 − 0.7071i −0.7071 + 0.7071i 3 −0.7071 + 0.7071i0.7071 − 0.7071i −0.7071 − 0.7071i 4  0.7071 + 0.7071i 0.7071 − 0.7071i−0.7071 − 0.7071i 5 −0.7071 + 0.7071i 0.7071 − 0.7071i −0.7071 − 0.7071i6  0.7071 + 0.7071i −0.7071 − 0.7071i   0.7071 + 0.7071i 7 −0.7071 −0.7071i 0.7071 − 0.7071i −0.7071 − 0.7071i 8 −0.7071 + 0.7071i −0.7071 +0.7071i  −0.7071 − 0.7071i 9  0.7071 + 0.7071i −0.7071 + 0.7071i −0.7071 + 0.7071i 10 −0.7071 + 0.7071i 0.7071 + 0.7071i  0.7071 −0.7071i 11  0.7071 + 0.7071i 0.7071 − 0.7071i  0.7071 + 0.7071i 12 0.7071 + 0.7071i 0.7071 + 0.7071i  0.7071 + 0.7071i 13 −0.7071 +0.7071i −0.7071 + 0.7071i   0.7071 + 0.7071i 14 −0.7071 + 0.7071i−0.7071 + 0.7071i  −0.7071 + 0.7071i 15  0.7071 − 0.7071i −0.7071 +0.7071i   0.7071 + 0.7071i 16  0.7071 − 0.7071i 0.7071 − 0.7071i  0.7071− 0.7071i 17 −0.7071 − 0.7071i 0.7071 + 0.7071i −0.7071 + 0.7071i 18 0.7071 + 0.7071i 0.7071 + 0.7071i −0.7071 − 0.7071i 19 −0.7071 −0.7071i −0.7071 − 0.7071i  −0.7071 − 0.7071i 20  0.7071 − 0.7071i0.7071 + 0.7071i  0.7071 + 0.7071i 21 −0.7071 + 0.7071i −0.7071 +0.7071i  −0.7071 + 0.7071i 22  0.7071 + 0.7071i 0.7071 − 0.7071i 0.7071 + 0.7071i 23  0.7071 + 0.7071i −0.7071 − 0.7071i   0.7071 +0.7071i 24 −0.7071 + 0.7071i −0.7071 + 0.7071i  −0.7071 − 0.7071i

element 1 0.7071 − 0.7071i  0.7071 − 0.7071i 2 0.7071 − 0.7071i 0.7071 + 0.7071i 3 0.7071 − 0.7071i −0.7071 − 0.7071i 4 −0.7071 −0.7071i  −0.7071 − 0.7071i 5 −0.7071 − 0.7071i  −0.7071 + 0.7071i 60.7071 − 0.7071i  0.7071 − 0.7071i 7 0.7071 + 0.7071i −0.7071 + 0.7071i8 0.7071 + 0.7071i  0.7071 − 0.7071i 9 −0.7071 + 0.7071i   0.7071 −0.7071i 10 −0.7071 + 0.7071i  −0.7071 − 0.7071i 11 0.7071 − 0.7071i−0.7071 − 0.7071i 12 −0.7071 + 0.7071i  −0.7071 − 0.7071i 13 0.7071 −0.7071i  0.7071 − 0.7071i 14 0.7071 + 0.7071i −0.7071 − 0.7071i 150.7071 − 0.7071i −0.7071 − 0.7071i 16 −0.7071 − 0.7071i   0.7071 +0.7071i 17 0.7071 + 0.7071i  0.7071 − 0.7071i 18 0.7071 − 0.7071i 0.7071 + 0.7071i 19 −0.7071 − 0.7071i  −0.7071 + 0.7071i 20 −0.7071 −0.7071i  −0.7071 + 0.7071i 21 0.7071 + 0.7071i  0.7071 − 0.7071i 22−0.7071 − 0.7071i   0.7071 + 0.7071i 23 0.7071 − 0.7071i  0.7071 −0.7071i 24 0.7071 − 0.7071i −0.7071 + 0.7071i

A method as in any above, where the at least one saved sequence is usedfor sequence modulation on a physical uplink control channel. A methodas in any above, where the at least one saved sequence is used fordemodulation and sounding of at least one reference signal. A method asin the previous, where said reference signals have a length of 12. Amethod as in any above, where the at least one saved sequence isallocated using higher layer signaling (e.g., radio resource controlsignaling). A method as in any above, where the at least one savedsequence comprises at least one sequence index. A method as in theprevious, where said at least one sequence index is cell-specific. Amethod as in any above, where the at least one saved sequence comprisesat least one cell-specific sequence index. A method as in any above,where two consecutive cyclic shifts are used in multi-code modulationbased on the at least one saved sequence.

A method as in any above, where the at least one saved sequencecomprises at least one zero auto-correlation sequence. A method as inany above, where the at least one saved sequence comprises at least onerandom zero auto-correlation sequence. A method as in any above, wherethe at least one saved sequence comprises at least one random zeroauto-correlation-like sequence. A method as in any above, where the atleast one random zero auto-correlation-like sequence consists of 30sequences. A method as in any above, where said at least one random zeroauto-correlation-like sequence has a length of one resource block or tworesource blocks. A method as in any above, where said at least onerandom zero auto-correlation-like sequence comprises at least one offirst sequences having a length of 12 sequence elements or secondsequences having a length of 24 sequence elements. A method as in anyabove, where the sequence elements of the at least one saved sequencecomprise values restricted such that said values can be represented withtwo bits.

A method as in any above, where the at least one saved sequence is usedfor sequence modulation for at least one communication transmitted froma mobile station. A method as in any above, where the at least one savedsequence is used for sequence modulation for at least one communicationreceived by a mobile station. A method as in any above, where the atleast one saved sequence is used for sequence modulation for at leastone communication transmitted from a base station. A method as in anyabove, where the at least one saved sequence is used for sequencemodulation for at least one communication received by a base station. Amethod as in any above, where the at least one saved sequence is usedfor at least one wireless communication within an evolved universalterrestrial radio access network.

A method as in any above, where each sequence element of the sequencesin the selected set of sequences has a frequency selected from QPSKconstellation points on a unit circle in a complex plane. A method as inany above, where each sequence element of the sequences in the selectedset of sequences has a frequency selected from four possible QPSKconstellation points on a unit circle in a complex plane. A method as inany above, where randomly selecting the set of sequences comprisesrandomly selecting in a frequency domain. A method as in any above,where randomly selecting the set of sequences comprises randomlyselecting only in a frequency domain. A method as in any above, wherecyclic shifts of the sequences in the selected set of sequences areorthogonal to one another.

A method as in any above, where the at least one saved sequencecomprises a plurality of saved sequences, the method further comprising:selecting a subset of the at least one saved sequence.

A method as in the previous, where selecting the subset of the pluralityof saved sequences comprises: calculating cross-correlations for eachpair of sequences of the plurality of saved sequences for a plurality ofdifferent cyclic shift combinations; selecting a cross-correlation valuehaving a largest amplitude as a cross-correlation representative valuefor the cross-correlations between the corresponding pair of sequences;and iterating the sequences of the plurality of saved sequences in thefollowing manner to obtain the subset of the plurality of savedsequences, where zero or more of the sequences of the plurality of savedsequences are removed on each iteration: for each sequence of theplurality of saved sequences, counting a first number of representativevalues exceeding a first cross-correlation threshold, a second number ofrepresentative values exceeding a second cross-correlation threshold anda third number of representative values exceeding a thirdcross-correlation threshold, where the first cross-correlation thresholdis greater than the second cross-correlation threshold and the secondcross-correlation threshold is greater than the third cross-correlationthreshold; selecting for further consideration those sequences havingthe first number of representative values equal to a maximum firstnumber of representative values over all sequences under consideration;selecting for further consideration those sequences having the secondnumber of representative values equal to a maximum second number ofrepresentative values over all sequences under consideration; removing asequence having a largest third number of representative values over allsequences under consideration; removing the cross-correlationrepresentative values related to the removed sequence; and placingremaining sequences back under consideration.

A method as in any above, where selecting the subset of the plurality ofsaved sequences comprises: calculating cross-correlations for each pairof sequences of the plurality of saved sequences for a plurality ofdifferent cyclic shift combinations; selecting a cross-correlation valuehaving a largest amplitude as a cross-correlation representative valuefor the cross-correlations between the corresponding pair of sequences;and iterating the sequences of the plurality of saved sequences in thefollowing manner to obtain the subset of the plurality of savedsequences, where zero or more of the sequences of the plurality of savedsequences are removed on each iteration: for each sequence of theplurality of saved sequences, counting p numbers of representativevalues exceeding p different cross-correlation thresholds; selecting forfurther consideration those sequences having the p−p+1 number ofrepresentative values equal to a maximum p-p+1 number of representativevalues over all sequences under consideration; selecting for furtherconsideration those sequences having the p−p+2 number of representativevalues equal to a maximum p−p+2 number of representative values over allsequences under consideration; and so on through the p−1 number ofrepresentative values; removing a sequence having a largest p-th numberof representative values over all sequences under consideration;removing the cross-correlation representative values related to theremoved sequence; and placing remaining sequences back underconsideration.

A method as in any above, where calculating cross-correlations comprisescalculating cross-correlations for each pair of sequences of theplurality of saved sequences for all cyclic shift combinations. A methodas in any above, the method further comprising: selecting the first,second and third cross-correlation thresholds. A method as in any above,where iteration of the sequences of the plurality of saved sequences isperformed until there remain a desired number of sequences or nosequences are found to be removed. A method as in any above, where thezero or more of the sequences of the plurality of saved sequences thatare removed on each iteration consists of one sequence.

A method as in any above, where selecting the subset of the plurality ofsaved sequences comprises: calculating cross-correlations for each pairof sequences of the plurality of saved sequences for a first pluralityof different cyclic shift combinations; selecting a cross-correlationvalue having a largest amplitude as a cross-correlation representativevalue for the cross-correlations between the corresponding pair ofsequences; for each pair of sequences, calculating mean squareddifference between the cross-correlations and m/sqrt(N) over a secondplurality of different cyclic shift combination, where m comprises ascaling factor and N comprises a sequence length; iterating thesequences of the plurality of saved sequences in the following manner toobtain the subset of the plurality of saved sequences, where zero ormore of the sequences of the plurality of saved sequences are removed oneach iteration: for each sequence of the plurality of saved sequences,counting a number of representative values exceeding a cross-correlationthreshold; selecting for further consideration those sequences havingthe number of representative values equal to a maximum number ofrepresentative values over all sequences under consideration; removing asequence having a largest mean squared difference over all sequencesunder consideration; removing the cross-correlation representativevalues and the mean squared difference values related to the removedsequence; and placing remaining sequences back under consideration.

A method as in any above, where selecting the subset of the plurality ofsaved sequences comprises: calculating cross-correlations for each pairof sequences of the plurality of saved sequences for a first pluralityof different cyclic shift combinations; selecting a cross-correlationvalue having a largest amplitude as a cross-correlation representativevalue for the cross-correlations between the corresponding pair ofsequences; for each pair of sequences, calculating meancross-correlation between the pair of sequences; iterating the sequencesof the plurality of saved sequences in the following manner to obtainthe subset of the plurality of saved sequences, where zero or more ofthe sequences of the plurality of saved sequences are removed on eachiteration: for each sequence of the plurality of saved sequences,counting a number of representative values exceeding a cross-correlationthreshold; selecting for further consideration those sequences havingthe number of representative values equal to a maximum number ofrepresentative values over all sequences under consideration; removing asequence having a largest mean cross-correlation over all sequencesunder consideration; removing the cross-correlation representativevalues and the mean cross-correlation values related to the removedsequence; and placing remaining sequences back under consideration.

A method as in any above, where calculating cross-correlations comprisescalculating cross-correlations for each pair of sequences of theplurality of saved sequences for all cyclic shift combinations. A methodas in any above, where iteration of the sequences of the plurality ofsaved sequences is performed until there remain a desired number ofsequences or no sequences are found to be removed. A method as in anyabove, where the zero or more of the sequences of the plurality of savedsequences that are removed on each iteration consists of one sequence. Amethod as in any above, where the first plurality of different cyclicshift combinations comprises the second plurality of different cyclicshift combinations. A method as in any above, the method furthercomprising: selecting at least one of the cross-correlation threshold orthe scaling factor m. A method as in any above, where a value 1/sqrt(N)comprises a cross-correlation value between Zadoff-Chu sequences.

A method as in any above, the method further comprising: using theselected subset for at least one wireless communication.

A method as in any above, where the subset of the plurality of savedsequences is used for sequence modulation on a physical uplink controlchannel. A method as in any above, where the subset of the plurality ofsaved sequences is used for demodulation and sounding of at least onereference signal. A method as in the previous, where said referencesignals have a length of 12. A method as in any above, where the subsetof the plurality of saved sequences is allocated using higher layersignaling (e.g., radio resource control signaling). A method as in anyabove, where the subset of the plurality of saved sequences at least onesequence index. A method as in the previous, where said at least onesequence index is cell-specific. A method as in any above, where thesubset of the plurality of saved sequences comprises at least onecell-specific sequence index. A method as in any above, where twoconsecutive cyclic shifts are used in multi-code modulation based on thesubset of the plurality of saved sequences.

A method as in any above, where the subset of the plurality of savedsequences comprises at least one zero auto-correlation sequence. Amethod as in any above, where the subset of the plurality of savedsequences comprises at least one random zero auto-correlation sequence.A method as in any above, where the subset of the plurality of savedsequences comprises at least one random zero auto-correlation-likesequence. A method as in any above, where the at least one zeroauto-correlation-like sequence consists of 30 sequences. A method as inany above, where said at least one random zero auto-correlation-likesequence has a length of one resource block or two resource blocks. Amethod as in any above, where said at least one random zeroauto-correlation-like sequences comprises at least one of firstsequences having a length of 12 sequence elements or second sequenceshaving a length of 24 sequence elements. A method as in any above, wherethe sequence elements of the subset of the plurality of saved sequencescomprise values restricted such that said values can be represented withtwo bits.

A method as in any above, where the subset of the plurality of savedsequences is used for sequence modulation for at least one communicationtransmitted from a mobile station. A method as in any above, where thesubset of the plurality of saved sequences is used for sequencemodulation for at least one communication received by a mobile station.A method as in any above, where the subset of the plurality of savedsequences is used for sequence modulation for at least one communicationtransmitted from a base station. A method as in any above, where thesubset of the plurality of saved sequences is used for sequencemodulation for at least one communication received by a base station. Amethod as in any above, where the subset of the plurality of savedsequences is used for at least one wireless communication within anevolved universal terrestrial radio access network.

A method as in any above, wherein the method is implemented by acomputer program. A method as in any above, wherein the method isimplemented by a program of instructions tangibly embodied on a programstorage device readable by a machine, said program of instructionsexecutable by the machine for performing operations, said operationscomprising steps of the method. A method as in any of the above, andfurther comprising one or more additional aspects of the exemplaryembodiments as described elsewhere herein.

-   (2) In another non-limiting, exemplary embodiment, a program storage    device readable by a machine, tangibly embodying a program of    instructions executable by the machine for performing operations,    said operations comprising: randomly selecting a set of sequences    with each sequence comprised of sequence elements, each sequence    element having a frequency selected from constellation points on a    unit circle in a complex plane, where the selected set of sequences    comprises a candidate set of sequences (801); calculating a first    cubic metric for each sequence of the candidate set of sequences,    where the first cubic metric is for single code modulation (802);    and in response to the first cubic metric being larger than at least    one threshold, removing the corresponding sequence from the    candidate set of sequences to obtain at least one saved sequence    (803).

A program storage device as in the previous, and further comprising oneor more additional aspects of the exemplary embodiments as describedelsewhere herein, such as those further aspects described above withrespect to one or more exemplary methods (i.e., number (1) above).

-   (3) In another non-limiting, exemplary embodiment, an apparatus    comprising: a memory and at least one processor, where the at least    one processor is configured to: randomly select a set of sequences    with each sequence comprised of sequence elements, each sequence    element having a frequency selected from constellation points on a    unit circle in a complex plane, where the selected set of sequences    comprises a candidate set of sequences; calculate a first cubic    metric for each sequence of the candidate set of sequences, where    the first cubic metric is for single code modulation; and in    response to the first cubic metric being larger than at least one    threshold, remove the corresponding sequence from the candidate set    of sequences to obtain at least one saved sequence, where the at    least one saved sequence is stored on the memory.

An apparatus as in the previous, and further comprising one or moreadditional aspects of the exemplary embodiments as described elsewhereherein, such as those further aspects described above with respect toone or more exemplary methods (i.e., number (1) above). An apparatus asin any above, further comprising at least one of a transceiver or anantenna. An apparatus as in any above, embodied in an integratedcircuit.

-   (4) In another non-limiting, exemplary embodiment, an apparatus    comprising: means for randomly selecting a set of sequences with    each sequence comprised of sequence elements, each sequence element    having a frequency selected from constellation points on a unit    circle in a complex plane, where the selected set of sequences    comprises a candidate set of sequences; means for calculating a    first cubic metric for each sequence of the candidate set of    sequences, where the first cubic metric is for single code    modulation; and means, in response to the first cubic metric being    larger than at least one threshold, for removing the corresponding    sequence from the candidate set of sequences to obtain at least one    saved sequence.

An apparatus as in the previous, and further comprising one or moreadditional aspects of the exemplary embodiments as described elsewhereherein, such as those further aspects described above with respect toone or more exemplary methods (i.e., number (1) above). An apparatus asin any above, further comprising means for communicating, such as meansfor transmitting and/or means for receiving, as non-limiting examples.An apparatus as in any above, embodied in an integrated circuit. Anapparatus as in any above, further comprising means for storing the atleast one saved sequence. An apparatus as in the previous, where themeans for storing comprises a memory. An apparatus as in any above,where the means for randomly selecting, the means for calculating andthe means for removing comprise at least one processor.

-   (5) In another non-limiting, exemplary embodiment, an apparatus    comprising: first circuitry configured to randomly select a set of    sequences with each sequence comprised of sequence elements, each    sequence element having a frequency selected from constellation    points on a unit circle in a complex plane, where the selected set    of sequences comprises a candidate set of sequences; second    circuitry configured to calculate a first cubic metric for each    sequence of the candidate set of sequences, where the first cubic    metric is for single code modulation; and third circuitry    configured, in response to the first cubic metric being larger than    at least one threshold, to remove the corresponding sequence from    the candidate set of sequences to obtain at least one saved    sequence.

An apparatus as in the previous, and further comprising one or moreadditional aspects of the exemplary embodiments as described elsewhereherein, such as those further aspects described above with respect toone or more exemplary methods (i.e., number (1) above). An apparatus asin any above, further comprising communication circuitry configured toat least one of transmit or receive communications to or from anotherapparatus. An apparatus as in any above, embodied in an integratedcircuit. An apparatus as in any above, further comprising storagecircuitry configured to store the at least one saved sequence.

-   (6) In another non-limiting, exemplary embodiment, and as shown in    FIG. 12, a method comprising: randomly selecting a set of sequences    with each sequence comprised of sequence elements, each sequence    element having a frequency selected from constellation points on a    unit circle in a complex plane, where the selected set of sequences    comprises a candidate set of sequences (901); calculating a first    cubic metric and a second cubic metric for each sequence of the    candidate set of sequences, where the first cubic metric is for    single code modulation and the second cubic metric is for multi-code    modulation (902); and in response to at least one of the first cubic    metric or the second cubic metric being larger than at least one    threshold, removing the corresponding sequence from the candidate    set of sequences to obtain at least one saved sequence (903).

A method as in the previous, and further comprising one or moreadditional aspects of the exemplary embodiments as described elsewhereherein, such as those further aspects described above with respect toone or more exemplary methods (i.e., number (1) above). A method as inany above, implemented by a computer program or an apparatus, similar toone or more of those exemplary embodiments identified above as (2), (3),(4) and/or (5).

-   (7) In another non-limiting, exemplary embodiment, and as shown in    FIG. 13, a method comprising: randomly selecting a set of sequences    with each sequence comprised of sequence elements, each sequence    element having a frequency selected from constellation points on a    unit circle in a complex plane, where the selected set of sequences    comprises a candidate set of sequences (951); calculating a first    cubic metric for each sequence of the candidate set of sequences,    where the first cubic metric is for single code modulation (952);    and based on at least one comparison of the first cubic metric to at    least one threshold, removing an unsuitable corresponding sequence    from the candidate set of sequences to obtain at least one saved    sequence (953).

A method as in the previous, where an unsuitable corresponding sequencecomprises a sequence having a first cubic metric larger than the atleast one threshold. A method as in any of the above, and furthercomprising one or more additional aspects of the exemplary embodimentsas described elsewhere herein, such as those further aspects describedabove with respect to one or more exemplary methods (i.e., number (1)above). A method as in any above, implemented by a computer program oran apparatus, similar to one or more of those exemplary embodimentsidentified above as (2), (3), (4), (5) and/or (6).

The exemplary embodiments of the invention, as discussed above and asparticularly described with respect to exemplary methods, may beimplemented as a computer program product comprising programinstructions embodied on a tangible computer-readable medium. Executionof the program instructions results in operations comprising steps ofutilizing the exemplary embodiments or steps of the method.

The exemplary embodiments of the invention, as discussed above and asparticularly described with respect to exemplary methods, may beimplemented in conjunction with a program storage device readable by amachine, tangibly embodying a program of instructions executable by themachine for performing operations. The operations comprise steps ofutilizing the exemplary embodiments or steps of the method.

It should be noted that the terms “connected,” “coupled,” or any variantthereof, mean any connection or coupling, either direct or indirect,between two or more elements, and may encompass the presence of one ormore intermediate elements between two elements that are “connected” or“coupled” together. The coupling or connection between the elements canbe physical, logical, or a combination thereof. As employed herein twoelements may be considered to be “connected” or “coupled” together bythe use of one or more wires, cables and/or printed electricalconnections, as well as by the use of electromagnetic energy, such aselectromagnetic energy having wavelengths in the radio frequency region,the microwave region and the optical (both visible and invisible)region, as several non-limiting and non-exhaustive examples.

In general, the various exemplary embodiments may be implemented inhardware or special purpose circuits, software, logic or any combinationthereof. For example, some aspects may be implemented in hardware, whileother aspects may be implemented in firmware or software which may beexecuted by a controller, microprocessor or other computing device,although the invention is not limited thereto. While various aspects ofthe exemplary embodiments of this invention may be illustrated anddescribed as block diagrams, flow charts, or using some other pictorialrepresentation, it is well understood that these blocks, apparatus,systems, techniques or methods described herein may be implemented in,as non-limiting examples, hardware, software, firmware, special purposecircuits or logic, general purpose hardware or controller or othercomputing devices, or some combination thereof.

Note further that the blocks shown in the logic flow diagrams of FIGS.4, 7, 10 and 11 may also be viewed as a plurality of interconnectedfunctional circuits/functions that operate as described.

As was noted above, it should be appreciated that at least some aspectsof the exemplary embodiments of the inventions may be practiced invarious components such as integrated circuit chips and modules. Thedesign of integrated circuits is by and large a highly automatedprocess. Complex and powerful software tools are available forconverting a logic level design into a semiconductor circuit designready to be etched and formed on a semiconductor substrate.

Programs, such as those provided by Synopsys, Inc. of Mountain View,Calif. and Cadence Design, of San Jose, Calif. automatically routeconductors and locate components on a semiconductor chip using wellestablished rules of design as well as libraries of pre-stored designmodules. Once the design for a semiconductor circuit has been completed,the resultant design, in a standardized electronic format (e.g., Opus,GDSII, or the like) may be transmitted to a semiconductor fabricationfacility or “fab” for fabrication.

Various modifications and adaptations to the foregoing exemplaryembodiments of this invention may become apparent to those skilled inthe relevant arts in view of the foregoing description, when read inconjunction with the accompanying drawings. However, any and allmodifications will still fall within the scope of the non-limiting andexemplary embodiments of this invention.

As but one example, while the exemplary embodiments have been describedabove in the context of the E-UTRAN (UTRAN-LTE) system, it should beappreciated that the exemplary embodiments of this invention are notlimited for use with only this one particular type of wirelesscommunication system, and that they may be used to advantage in otherwireless communication systems. Further, the exemplary embodiments ofthis invention are not constrained for use with any specific frameformat, numbers of long blocks within a frame, sub-carrier mappingscheme, type of modulation and/or precoding technique, as non-limitingexamples, that may have been referred to above.

In addition, some of the features of the various non-limiting andexemplary embodiments of this invention may be used to advantage withoutthe corresponding use of other features. As such, the foregoingdescription should be considered as merely illustrative of theprinciples, teachings and exemplary embodiments of this invention, andnot in limitation thereof.

What is claimed is:
 1. A method comprising: randomly selecting a set ofsequences with each sequence comprised of sequence elements, eachsequence element having a frequency selected from constellation pointson a unit circle in a complex plane, where the selected set of sequencescomprises a candidate set of sequences; calculating a first cubic metricfor each sequence of the candidate set of sequences, where the firstcubic metric is for single code modulation; and in response to the firstcubic metric being larger than at least one threshold, removing thecorresponding sequence from the candidate set of sequences to obtain atleast one saved sequence.
 2. A method as in claim 1, further comprising:calculating a second cubic metric for each sequence of the candidate setof sequences, where the second cubic metric is for multi-codemodulation; and in response to at least one of the first cubic metric orthe second cubic metric being larger than the at least one threshold,removing the corresponding sequence from the candidate set of sequencesto obtain the at least one saved sequence.
 3. A method as in claim 2,where the at least one threshold comprises a first threshold and asecond threshold, where removing the corresponding sequence is performedin response to at least one of the first cubic metric being larger thanthe first threshold or the second cubic metric being larger than thesecond threshold.
 4. A method as in claim 1, further comprising:calculating cross-correlations for a plurality of different cyclic shiftcombinations of each sequence of the candidate set of sequences againsta second sequence set; selecting a cross-correlation value having alargest amplitude as a representative cross-correlation value for thecross-correlations between the corresponding sequence and the secondsequence set; and in response to the representative cross-correlationvalue being larger than a threshold, removing the corresponding sequencefrom the candidate set of sequences.
 5. A method as in claim 4, wherethe second sequence set is comprised of second sequences having a lengthof 36 sequence elements or second sequences having a length of 12sequence elements.
 6. A method as in claim 1, where the at least onesaved sequence is used for sequence modulation on a physical uplinkcontrol channel.
 7. A method as in claim 1, where two consecutive cyclicshifts are used in multi-code modulation based on the at least one savedsequence.
 8. A method as in claim 1, where the at least one savedsequence comprises a plurality of random zero auto-correlation-likesequences.
 9. A method as in claim 1, where each sequence element of thesequences in the selected set of sequences has a frequency selected fromfour possible constellation points on a unit circle.
 10. A method as inclaim 1, where the at least one saved sequence has a length of oneresource block or two resource blocks.
 11. A method as in claim 1, wherethe at least one saved sequence comprises at least one of: element 1 0.7071 − 0.7071i −0.7071 + 0.7071i  0.7071 + 0.7071i 0.7071 + 0.7071i 2−0.7071 + 0.7071i  0.7071 + 0.7071i  0.7071 + 0.7071i −0.7071 + 0.7071i 3  0.7071 − 0.7071i  0.7071 − 0.7071i −0.7071 − 0.7071i 0.7071 + 0.7071i4  0.7071 + 0.7071i  0.7071 − 0.7071i −0.7071 − 0.7071i 0.7071 − 0.7071i5 −0.7071 − 0.7071i −0.7071 + 0.7071i −0.7071 − 0.7071i 0.7071 + 0.7071i6 −0.7071 − 0.7071i −0.7071 + 0.7071i −0.7071 − 0.7071i −0.7071 +0.7071i  7 −0.7071 − 0.7071i −0.7071 − 0.7071i  0.7071 − 0.7071i−0.7071 + 0.7071i  8 −0.7071 − 0.7071i  0.7071 + 0.7071i −0.7071 +0.7071i −0.7071 + 0.7071i  9 −0.7071 − 0.7071i −0.7071 + 0.7071i −0.7071− 0.7071i 0.7071 − 0.7071i 10  0.7071 + 0.7071i  0.7071 + 0.7071i 0.7071 + 0.7071i 0.7071 − 0.7071i 11  0.7071 − 0.7071i −0.7071 +0.7071i −0.7071 − 0.7071i −0.7071 + 0.7071i  12 −0.7071 − 0.7071i−0.7071 + 0.7071i −0.7071 + 0.7071i 0.7071 − 0.7071i element 1 −0.7071 −0.7071i −0.7071 − 0.7071i  0.7071 + 0.7071i 2 −0.7071 + 0.7071i 0.7071 + 0.7071i −0.7071 + 0.7071i 3  0.7071 + 0.7071i  0.7071 +0.7071i −0.7071 + 0.7071i 4  0.7071 + 0.7071i −0.7071 + 0.7071i−0.7071 + 0.7071i 5 −0.7071 − 0.7071i −0.7071 − 0.7071i  0.7071 −0.7071i 6  0.7071 + 0.7071i −0.7071 + 0.7071i  0.7071 − 0.7071i 7−0.7071 − 0.7071i −0.7071 − 0.7071i −0.7071 − 0.7071i 8 −0.7071 −0.7071i −0.7071 − 0.7071i −0.7071 − 0.7071i 9  0.7071 − 0.7071i−0.7071 + 0.7071i  0.7071 + 0.7071i 10  0.7071 − 0.7071i  0.7071 +0.7071i −0.7071 − 0.7071i 11  0.7071 + 0.7071i −0.7071 + 0.7071i−0.7071 + 0.7071i 12 −0.7071 − 0.7071i  0.7071 − 0.7071i  0.7071 −0.7071i.


12. A method as in claim 1, where the at least one saved sequencecomprises at least one of: element 1 −0.7071 − 0.7071i −0.7071 +0.7071i  −0.7071 − 0.7071i 2 −0.7071 − 0.7071i 0.7071 − 0.7071i−0.7071 + 0.7071i 3 −0.7071 + 0.7071i 0.7071 − 0.7071i −0.7071 − 0.7071i4  0.7071 + 0.7071i 0.7071 − 0.7071i −0.7071 − 0.7071i 5 −0.7071 +0.7071i 0.7071 − 0.7071i −0.7071 − 0.7071i 6  0.7071 + 0.7071i −0.7071 −0.7071i   0.7071 + 0.7071i 7 −0.7071 − 0.7071i 0.7071 − 0.7071i −0.7071− 0.7071i 8 −0.7071 + 0.7071i −0.7071 + 0.7071i  −0.7071 − 0.7071i 9 0.7071 + 0.7071i −0.7071 + 0.7071i  −0.7071 + 0.7071i 10 −0.7071 +0.7071i 0.7071 + 0.7071i  0.7071 − 0.7071i 11  0.7071 + 0.7071i 0.7071 −0.7071i  0.7071 + 0.7071i 12  0.7071 + 0.7071i 0.7071 + 0.7071i 0.7071 + 0.7071i 13 −0.7071 + 0.7071i −0.7071 + 0.7071i   0.7071 +0.7071i 14 −0.7071 + 0.7071i −0.7071 + 0.7071i  −0.7071 + 0.7071i 15 0.7071 − 0.7071i −0.7071 + 0.7071i   0.7071 + 0.7071i 16  0.7071 −0.7071i 0.7071 − 0.7071i  0.7071 − 0.7071i 17 −0.7071 − 0.7071i 0.7071 +0.7071i −0.7071 + 0.7071i 18  0.7071 + 0.7071i 0.7071 + 0.7071i −0.7071− 0.7071i 19 −0.7071 − 0.7071i −0.7071 − 0.7071i  −0.7071 − 0.7071i 20 0.7071 − 0.7071i 0.7071 + 0.7071i  0.7071 + 0.7071i 21 −0.7071 +0.7071i −0.7071 + 0.7071i  −0.7071 + 0.7071i 22  0.7071 + 0.7071i 0.7071− 0.7071i  0.7071 + 0.7071i 23  0.7071 + 0.7071i −0.7071 − 0.7071i  0.7071 + 0.7071i 24 −0.7071 + 0.7071i −0.7071 + 0.7071i  −0.7071 −0.7071i

element 1 0.7071 − 0.7071i  0.7071 − 0.7071i 2 0.7071 − 0.7071i 0.7071 + 0.7071i 3 0.7071 − 0.7071i −0.7071 − 0.7071i 4 −0.7071 −0.7071i  −0.7071 − 0.7071i 5 −0.7071 − 0.7071i  −0.7071 + 0.7071i 60.7071 − 0.7071i  0.7071 − 0.7071i 7 0.7071 + 0.7071i −0.7071 + 0.7071i8 0.7071 + 0.7071i  0.7071 − 0.7071i 9 −0.7071 + 0.7071i   0.7071 −0.7071i 10 −0.7071 + 0.7071i  −0.7071 − 0.7071i 11 0.7071 − 0.7071i−0.7071 − 0.7071i 12 −0.7071 + 0.7071i  −0.7071 − 0.7071i 13 0.7071 −0.7071i  0.7071 − 0.7071i 14 0.7071 + 0.7071i −0.7071 − 0.7071i 150.7071 − 0.7071i −0.7071 − 0.7071i 16 −0.7071 − 0.7071i   0.7071 +0.7071i 17 0.7071 + 0.7071i  0.7071 − 0.7071i 18 0.7071 − 0.7071i 0.7071 + 0.7071i 19 −0.7071 − 0.7071i  −0.7071 + 0.7071i 20 −0.7071 −0.7071i  −0.7071 + 0.7071i 21 0.7071 + 0.7071i  0.7071 − 0.7071i 22−0.7071 − 0.7071i   0.7071 + 0.7071i 23 0.7071 − 0.7071i  0.7071 −0.7071i 24 0.7071 − 0.7071i  −0.7071 + 0.7071i.


13. A method as in claim 1, where the at least one saved sequence isused for sequence modulation for at least one communication transmittedfrom a mobile station.
 14. A method as in claim 1, where the at leastone saved sequence is used for sequence modulation for at least onecommunication received by a base station.
 15. A method as in claim 1,where the at least one saved sequence is used for at least one wirelesscommunication within an evolved universal terrestrial radio accessnetwork.
 16. A method as in claim 1, where the at least one savedsequence comprises a plurality of saved sequences, the method furthercomprising: selecting a subset of the plurality of saved sequences. 17.A method as in claim 16, where selecting the subset of the plurality ofsaved sequences comprises: calculating cross-correlations for each pairof sequences of the plurality of saved sequences for a plurality ofdifferent cyclic shift combinations; selecting a cross-correlation valuehaving a largest amplitude as a cross-correlation representative valuefor the cross-correlations between the corresponding pair of sequences;and iterating the sequences of the plurality of saved sequences in thefollowing manner to obtain the subset of the plurality of savedsequences, where zero or more of the sequences of the plurality of savedsequences are removed on each iteration: for each sequence of theplurality of saved sequences, counting a first number of representativevalues exceeding a first cross-correlation threshold, a second number ofrepresentative values exceeding a second cross-correlation threshold anda third number of representative values exceeding a thirdcross-correlation threshold, where the first cross-correlation thresholdis greater than the second cross-correlation threshold and the secondcross-correlation threshold is greater than the third cross-correlationthreshold; selecting for further consideration those sequences havingthe first number of representative values equal to a maximum firstnumber of representative values over all sequences under consideration;selecting for further consideration those sequences having the secondnumber of representative values equal to a maximum second number ofrepresentative values over all sequences under consideration; removing asequence having a largest third number of representative values over allsequences under consideration; removing the cross-correlationrepresentative values related to the removed sequence; and placingremaining sequences back under consideration.
 18. A method as in claim16, where selecting the subset of the plurality of saved sequencescomprises: calculating cross-correlations for each pair of sequences ofthe plurality of saved sequences for a first plurality of differentcyclic shift combinations; selecting a cross-correlation value having alargest amplitude as a cross-correlation representative value for thecross-correlations between the corresponding pair of sequences; for eachpair of sequences, calculating mean squared difference between thecross-correlations and m/sqrt(N) over a second plurality of differentcyclic shift combination, where m comprises a scaling factor and Ncomprises a sequence length; iterating the sequences of the plurality ofsaved sequences in the following manner to obtain the subset of theplurality of saved sequences, where zero or more of the sequences of theplurality of saved sequences are removed on each iteration: for eachsequence of the plurality of saved sequences, counting a number ofrepresentative values exceeding a cross-correlation threshold; selectingfor further consideration those sequences having the number ofrepresentative values equal to a maximum number of representative valuesover all sequences under consideration; removing a sequence having alargest mean squared difference over all sequences under consideration;removing the cross-correlation representative values and the meansquared difference values related to the removed sequence; and placingremaining sequences back under consideration.
 19. A non-transitoryprogram storage device readable by a machine, tangibly embodying aprogram of instructions executable by the machine for performingoperations, said operations comprising: randomly selecting a set ofsequences with each sequence comprised of sequence elements, eachsequence element having a frequency selected from constellation pointson a unit circle in a complex plane, where the selected set of sequencescomprises a candidate set of sequences; calculating a first cubic metricfor each sequence of the candidate set of sequences, where the firstcubic metric is for single code modulation; and in response to the firstcubic metric being larger than at least one threshold, removing thecorresponding sequence from the candidate set of sequences to obtain atleast one saved sequence.
 20. A program storage device as in claim 19,further comprising: calculating a second cubic metric for each sequenceof the candidate set of sequences, where the second cubic metric is formulti-code modulation; and in response to at least one of the firstcubic metric or the second cubic metric being larger than the at leastone threshold, removing the corresponding sequence from the candidateset of sequences to obtain the at least one saved sequence.
 21. Aprogram storage device as in claim 20, where the at least one thresholdcomprises a first threshold and a second threshold, where removing thecorresponding sequence is performed in response to at least one of thefirst cubic metric being larger than the first threshold or the secondcubic metric being larger than the second threshold.
 22. A programstorage device as in claim 19, the operations further comprising:calculating cross-correlations for a plurality of different cyclic shiftcombinations of each sequence of the candidate set of sequences againsta second sequence set; selecting a cross-correlation value having alargest amplitude as a representative cross-correlation value for thecross-correlations between the corresponding sequence and the secondsequence set; and in response to the representative cross-correlationvalue being larger than a threshold, removing the corresponding sequencefrom the candidate set of sequences.
 23. A program storage device as inclaim 19, where the at least one saved sequence comprises at least oneof: element 1  0.7071 − 0.7071i −0.7071 + 0.7071i  0.7071 + 0.7071i0.7071 + 0.7071i 2 −0.7071 + 0.7071i  0.7071 + 0.7071i  0.7071 + 0.7071i−0.7071 + 0.7071i  3  0.7071 − 0.7071i  0.7071 − 0.7071i −0.7071 −0.7071i 0.7071 + 0.7071i 4  0.7071 + 0.7071i  0.7071 − 0.7071i −0.7071 −0.7071i 0.7071 − 0.7071i 5 −0.7071 − 0.7071i −0.7071 + 0.7071i −0.7071 −0.7071i 0.7071 + 0.7071i 6 −0.7071 − 0.7071i −0.7071 + 0.7071i −0.7071 −0.7071i −0.7071 + 0.7071i  7 −0.7071 − 0.7071i −0.7071 − 0.7071i  0.7071− 0.7071i −0.7071 + 0.7071i  8 −0.7071 − 0.7071i  0.7071 + 0.7071i−0.7071 + 0.7071i −0.7071 + 0.7071i  9 −0.7071 − 0.7071i −0.7071 +0.7071i −0.7071 − 0.7071i 0.7071 − 0.7071i 10  0.7071 + 0.7071i 0.7071 + 0.7071i  0.7071 + 0.7071i 0.7071 − 0.7071i 11  0.7071 −0.7071i −0.7071 + 0.7071i −0.7071 − 0.7071i −0.7071 + 0.7071i  12−0.7071 − 0.7071i −0.7071 + 0.7071i −0.7071 + 0.7071i 0.7071 − 0.7071ielement 1 −0.7071 − 0.7071i −0.7071 − 0.7071i  0.7071 + 0.7071i 2−0.7071 + 0.7071i  0.7071 + 0.7071i −0.7071 + 0.7071i 3  0.7071 +0.7071i  0.7071 + 0.7071i −0.7071 + 0.7071i 4  0.7071 + 0.7071i−0.7071 + 0.7071i −0.7071 + 0.7071i 5 −0.7071 − 0.7071i −0.7071 −0.7071i  0.7071 − 0.7071i 6  0.7071 + 0.7071i −0.7071 + 0.7071i  0.7071− 0.7071i 7 −0.7071 − 0.7071i −0.7071 − 0.7071i −0.7071 − 0.7071i 8−0.7071 − 0.7071i −0.7071 − 0.7071i −0.7071 − 0.7071i 9  0.7071 −0.7071i −0.7071 + 0.7071i  0.7071 + 0.7071i 10  0.7071 − 0.7071i 0.7071 + 0.7071i −0.7071 − 0.7071i 11  0.7071 + 0.7071i −0.7071 +0.7071i −0.7071 + 0.7071i 12 −0.7071 − 0.7071i  0.7071 − 0.7071i  0.7071− 0.7071i.


24. A program storage device as in claim 19, where the at least onesaved sequence comprises at least one of: element 1 −0.7071 − 0.7071i−0.7071 + 0.7071i  −0.7071 − 0.7071i 2 −0.7071 − 0.7071i 0.7071 −0.7071i −0.7071 + 0.7071i 3 −0.7071 + 0.7071i 0.7071 − 0.7071i −0.7071 −0.7071i 4  0.7071 + 0.7071i 0.7071 − 0.7071i −0.7071 − 0.7071i 5−0.7071 + 0.7071i 0.7071 − 0.7071i −0.7071 − 0.7071i 6  0.7071 + 0.7071i−0.7071 − 0.7071i   0.7071 + 0.7071i 7 −0.7071 − 0.7071i 0.7071 −0.7071i −0.7071 − 0.7071i 8 −0.7071 + 0.7071i −0.7071 + 0.7071i  −0.7071− 0.7071i 9  0.7071 + 0.7071i −0.7071 + 0.7071i  −0.7071 + 0.7071i 10−0.7071 + 0.7071i 0.7071 + 0.7071i  0.7071 − 0.7071i 11  0.7071 +0.7071i 0.7071 − 0.7071i  0.7071 + 0.7071i 12  0.7071 + 0.7071i 0.7071 +0.7071i  0.7071 + 0.7071i 13 −0.7071 + 0.7071i −0.7071 + 0.7071i  0.7071 + 0.7071i 14 −0.7071 + 0.7071i −0.7071 + 0.7071i  −0.7071 +0.7071i 15  0.7071 − 0.7071i −0.7071 + 0.7071i   0.7071 + 0.7071i 16 0.7071 − 0.7071i 0.7071 − 0.7071i  0.7071 − 0.7071i 17 −0.7071 −0.7071i 0.7071 + 0.7071i −0.7071 + 0.7071i 18  0.7071 + 0.7071i 0.7071 +0.7071i −0.7071 − 0.7071i 19 −0.7071 − 0.7071i −0.7071 − 0.7071i −0.7071 − 0.7071i 20  0.7071 − 0.7071i 0.7071 + 0.7071i  0.7071 +0.7071i 21 −0.7071 + 0.7071i −0.7071 + 0.7071i  −0.7071 + 0.7071i 22 0.7071 + 0.7071i 0.7071 − 0.7071i  0.7071 + 0.7071i 23  0.7071 +0.7071i −0.7071 − 0.7071i   0.7071 + 0.7071i 24 −0.7071 + 0.7071i−0.7071 + 0.7071i  −0.7071 − 0.7071i

element 1 0.7071 − 0.7071i  0.7071 − 0.7071i 2 0.7071 − 0.7071i 0.7071 + 0.7071i 3 0.7071 − 0.7071i −0.7071 − 0.7071i 4 −0.7071 −0.7071i  −0.7071 − 0.7071i 5 −0.7071 − 0.7071i  −0.7071 + 0.7071i 60.7071 − 0.7071i  0.7071 − 0.7071i 7 0.7071 + 0.7071i −0.7071 + 0.7071i8 0.7071 + 0.7071i  0.7071 − 0.7071i 9 −0.7071 + 0.7071i   0.7071 −0.7071i 10 −0.7071 + 0.7071i  −0.7071 − 0.7071i 11 0.7071 − 0.7071i−0.7071 − 0.7071i 12 −0.7071 + 0.7071i  −0.7071 − 0.7071i 13 0.7071 −0.7071i  0.7071 − 0.7071i 14 0.7071 + 0.7071i −0.7071 − 0.7071i 150.7071 − 0.7071i −0.7071 − 0.7071i 16 −0.7071 − 0.7071i   0.7071 +0.7071i 17 0.7071 + 0.7071i  0.7071 − 0.7071i 18 0.7071 − 0.7071i 0.7071 + 0.7071i 19 −0.7071 − 0.7071i  −0.7071 + 0.7071i 20 −0.7071 −0.7071i  −0.7071 + 0.7071i 21 0.7071 + 0.7071i  0.7071 − 0.7071i 22−0.7071 − 0.7071i   0.7071 + 0.7071i 23 0.7071 − 0.7071i  0.7071 −0.7071i 24 0.7071 − 0.7071i −0.7071 + 0.7071i.


25. A program storage device as in claim 19, where the at least onesaved sequence is used for at least one wireless communication within anevolved universal terrestrial radio access network.
 26. A programstorage device as in claim 19, where the at least one saved sequencecomprises a plurality of saved sequences, the operations furthercomprising: selecting a subset of the plurality of saved sequences,where selecting the subset of the plurality of saved sequencescomprises: calculating cross-correlations for each pair of sequences ofthe plurality of saved sequences for a plurality of different cyclicshift combinations; selecting a cross-correlation value having a largestamplitude as a cross-correlation representative value for thecross-correlations between the corresponding pair of sequences; anditerating the sequences of the plurality of saved sequences in thefollowing manner to obtain the subset of the plurality of savedsequences, where zero or more of the sequences of the plurality of savedsequences are removed on each iteration: for each sequence of theplurality of saved sequences, counting a first number of representativevalues exceeding a first cross-correlation threshold, a second number ofrepresentative values exceeding a second cross-correlation threshold anda third number of representative values exceeding a thirdcross-correlation threshold, where the first cross-correlation thresholdis greater than the second cross-correlation threshold and the secondcross-correlation threshold is greater than the third cross-correlationthreshold; selecting for further consideration those sequences havingthe first number of representative values equal to a maximum firstnumber of representative values over all sequences under consideration;selecting for further consideration those sequences having the secondnumber of representative values equal to a maximum second number ofrepresentative values over all sequences under consideration; removing asequence having a largest third number of representative values over allsequences under consideration; removing the cross-correlationrepresentative values related to the removed sequence; and placingremaining sequences back under consideration.
 27. A program storagedevice as in claim 19, where the at least one saved sequence comprises aplurality of saved sequences, the operations further comprising:selecting a subset of the plurality of saved sequences, where selectingthe subset of the plurality of saved sequences comprises: calculatingcross-correlations for each pair of sequences of the plurality of savedsequences for a first plurality of different cyclic shift combinations;selecting a cross-correlation value having a largest amplitude as across-correlation representative value for the cross-correlationsbetween the corresponding pair of sequences; for each pair of sequences,calculating mean squared difference between the cross-correlations andm/sqrt(N) over a second plurality of different cyclic shift combination,where m comprises a scaling factor and N comprises a sequence length;iterating the sequences of the plurality of saved sequences in thefollowing manner to obtain the subset of the plurality of savedsequences, where zero or more of the sequences of the plurality of savedsequences are removed on each iteration: for each sequence of theplurality of saved sequences, counting a number of representative valuesexceeding a cross-correlation threshold; selecting for furtherconsideration those sequences having the number of representative valuesequal to a maximum number of representative values over all sequencesunder consideration; removing a sequence having a largest mean squareddifference over all sequences under consideration; removing thecross-correlation representative values and the mean squared differencevalues related to the removed sequence; and placing remaining sequencesback under consideration.
 28. An apparatus comprising: a memory and atleast one processor, where the at least one processor is configured to:randomly select a set of sequences with each sequence comprised ofsequence elements, each sequence element having a frequency selectedfrom constellation points on a unit circle in a complex plane, where theselected set of sequences comprises a candidate set of sequences;calculate a first cubic metric for each sequence of the candidate set ofsequences, where the first cubic metric is for single code modulation;and in response to the first cubic metric being larger than at least onethreshold, remove the corresponding sequence from the candidate set ofsequences to obtain at least one saved sequence, where the at least onesaved sequence is stored on the memory.
 29. An apparatus as in claim 28,where the at least one processor is further configured to: calculate asecond cubic metric for each sequence of the candidate set of sequences,where the second cubic metric is for multi-code modulation; and inresponse to at least one of the first cubic metric or the second cubicmetric being larger than at least one threshold, remove thecorresponding sequence from the candidate set of sequences to obtain theat least one saved sequence.
 30. An apparatus as in claim 29, where theat least one threshold comprises a first threshold and a secondthreshold, where the at least one processor is configured to remove thecorresponding sequence in response to at least one of the first cubicmetric being larger than the first threshold or the second cubic metricbeing larger than the second threshold.
 31. An apparatus as in claim 28,where the processor is further configured to: calculatecross-correlations for a plurality of different cyclic shiftcombinations of each sequence of the candidate set of sequences againsta second sequence set; select a cross-correlation value having a largestamplitude as a representative cross-correlation value for thecross-correlations between the corresponding sequence and the secondsequence set; and in response to the representative cross-correlationvalue being larger than a threshold, remove the corresponding sequencefrom the candidate set of sequences.
 32. An apparatus as in claim 28,where the at least one saved sequence comprises at least one of: element1  0.7071 − 0.7071i −0.7071 + 0.7071i  0.7071 + 0.7071i 0.7071 + 0.7071i2 −0.7071 + 0.7071i  0.7071 + 0.7071i  0.7071 + 0.7071i −0.7071 +0.7071i  3  0.7071 − 0.7071i  0.7071 − 0.7071i −0.7071 − 0.7071i0.7071 + 0.7071i 4  0.7071 + 0.7071i  0.7071 − 0.7071i −0.7071 − 0.7071i0.7071 − 0.7071i 5 −0.7071 − 0.7071i −0.7071 + 0.7071i −0.7071 − 0.7071i0.7071 + 0.7071i 6 −0.7071 − 0.7071i −0.7071 + 0.7071i −0.7071 − 0.7071i−0.7071 + 0.7071i  7 −0.7071 − 0.7071i −0.7071 − 0.7071i  0.7071 −0.7071i −0.7071 + 0.7071i  8 −0.7071 − 0.7071i  0.7071 + 0.7071i−0.7071 + 0.7071i −0.7071 + 0.7071i  9 −0.7071 − 0.7071i −0.7071 +0.7071i −0.7071 − 0.7071i 0.7071 − 0.7071i 10  0.7071 + 0.7071i 0.7071 + 0.7071i  0.7071 + 0.7071i 0.7071 − 0.7071i 11  0.7071 −0.7071i −0.7071 + 0.7071i −0.7071 − 0.7071i −0.7071 + 0.7071i  12−0.7071 − 0.7071i −0.7071 + 0.7071i −0.7071 + 0.7071i 0.7071 − 0.7071ielement 1 −0.7071 − 0.7071i −0.7071 − 0.7071i  0.7071 + 0.7071i 2−0.7071 + 0.7071i  0.7071 + 0.7071i −0.7071 + 0.7071i 3  0.7071 +0.7071i  0.7071 + 0.7071i −0.7071 + 0.7071i 4  0.7071 + 0.7071i−0.7071 + 0.7071i −0.7071 + 0.7071i 5 −0.7071 − 0.7071i −0.7071 −0.7071i  0.7071 − 0.7071i 6  0.7071 + 0.7071i −0.7071 + 0.7071i  0.7071− 0.7071i 7 −0.7071 − 0.7071i −0.7071 − 0.7071i −0.7071 − 0.7071i 8−0.7071 − 0.7071i −0.7071 − 0.7071i −0.7071 − 0.7071i 9  0.7071 −0.7071i −0.7071 + 0.7071i  0.7071 + 0.7071i 10  0.7071 − 0.7071i 0.7071 + 0.7071i −0.7071 − 0.7071i 11  0.7071 + 0.7071i −0.7071 +0.7071i −0.7071 + 0.7071i 12 −0.7071 − 0.7071i  0.7071 − 0.7071i  0.7071− 0.7071i.


33. An apparatus as in claim 28, where the at least one saved sequencecomprises at least one of: element 1 −0.7071 − 0.7071i −0.7071 +0.7071i  −0.7071 − 0.7071i 2 −0.7071 − 0.7071i 0.7071 − 0.7071i−0.7071 + 0.7071i 3 −0.7071 + 0.7071i 0.7071 − 0.7071i −0.7071 − 0.7071i4  0.7071 + 0.7071i 0.7071 − 0.7071i −0.7071 − 0.7071i 5 −0.7071 +0.7071i 0.7071 − 0.7071i −0.7071 − 0.7071i 6  0.7071 + 0.7071i −0.7071 −0.7071i   0.7071 + 0.7071i 7 −0.7071 − 0.7071i 0.7071 − 0.7071i −0.7071− 0.7071i 8 −0.7071 + 0.7071i −0.7071 + 0.7071i  −0.7071 − 0.7071i 9 0.7071 + 0.7071i −0.7071 + 0.7071i  −0.7071 + 0.7071i 10 −0.7071 +0.7071i 0.7071 + 0.7071i  0.7071 − 0.7071i 11  0.7071 + 0.7071i 0.7071 −0.7071i  0.7071 + 0.7071i 12  0.7071 + 0.7071i 0.7071 + 0.7071i 0.7071 + 0.7071i 13 −0.7071 + 0.7071i −0.7071 + 0.7071i   0.7071 +0.7071i 14 −0.7071 + 0.7071i −0.7071 + 0.7071i  −0.7071 + 0.7071i 15 0.7071 − 0.7071i −0.7071 + 0.7071i   0.7071 + 0.7071i 16  0.7071 −0.7071i 0.7071 − 0.7071i  0.7071 − 0.7071i 17 −0.7071 − 0.7071i 0.7071 +0.7071i −0.7071 + 0.7071i 18  0.7071 + 0.7071i 0.7071 + 0.7071i −0.7071− 0.7071i 19 −0.7071 − 0.7071i −0.7071 − 0.7071i  −0.7071 − 0.7071i 20 0.7071 − 0.7071i 0.7071 + 0.7071i  0.7071 + 0.7071i 21 −0.7071 +0.7071i −0.7071 + 0.7071i  −0.7071 + 0.7071i 22  0.7071 + 0.7071i 0.7071− 0.7071i  0.7071 + 0.7071i 23  0.7071 + 0.7071i −0.7071 − 0.7071i  0.7071 + 0.7071i 24 −0.7071 + 0.7071i −0.7071 + 0.7071i  −0.7071 −0.7071i

element 1 0.7071 − 0.7071i  0.7071 − 0.7071i 2 0.7071 − 0.7071i 0.7071 + 0.7071i 3 0.7071 − 0.7071i −0.7071 − 0.7071i 4 −0.7071 −0.7071i  −0.7071 − 0.7071i 5 −0.7071 − 0.7071i  −0.7071 + 0.7071i 60.7071 − 0.7071i  0.7071 − 0.7071i 7 0.7071 + 0.7071i −0.7071 + 0.7071i8 0.7071 + 0.7071i  0.7071 − 0.7071i 9 −0.7071 + 0.7071i   0.7071 −0.7071i 10 −0.7071 + 0.7071i  −0.7071 − 0.7071i 11 0.7071 − 0.7071i−0.7071 − 0.7071i 12 −0.7071 + 0.7071i  −0.7071 − 0.7071i 13 0.7071 −0.7071i  0.7071 − 0.7071i 14 0.7071 + 0.7071i −0.7071 − 0.7071i 150.7071 − 0.7071i −0.7071 − 0.7071i 16 −0.7071 − 0.7071i   0.7071 +0.7071i 17 0.7071 + 0.7071i  0.7071 − 0.7071i 18 0.7071 − 0.7071i 0.7071 + 0.7071i 19 −0.7071 − 0.7071i  −0.7071 + 0.7071i 20 −0.7071 −0.7071i  −0.7071 + 0.7071i 21 0.7071 + 0.7071i  0.7071 − 0.7071i 22−0.7071 − 0.7071i   0.7071 + 0.7071i 23 0.7071 − 0.7071i  0.7071 −0.7071i 24 0.7071 − 0.7071i −0.7071 + 0.7071i.


34. An apparatus as in claim 28, further comprising a transceiver, wherethe at least one saved sequence is used for at least one wirelesscommunication, via the transceiver, within an evolved universalterrestrial radio access network.
 35. An apparatus as in claim 28, wherethe at least one saved sequence comprises a plurality of savedsequences, the at least one processor being further configured to selecta subset of the plurality of saved sequences, where the at least oneprocessor selecting the subset of the plurality of saved sequencescomprises the at least one processor: calculating cross-correlations foreach pair of sequences of the plurality of saved sequences for aplurality of different cyclic shift combinations; selecting across-correlation value having a largest amplitude as across-correlation representative value for the cross-correlationsbetween the corresponding pair of sequences; and iterating the sequencesof the plurality of saved sequences in the following manner to obtainthe subset of the plurality of saved sequences, where zero or more ofthe sequences of the plurality of saved sequences are removed on eachiteration: for each sequence of the plurality of saved sequences,counting a first number of representative values exceeding a firstcross-correlation threshold, a second number of representative valuesexceeding a second cross-correlation threshold and a third number ofrepresentative values exceeding a third cross-correlation threshold,where the first cross-correlation threshold is greater than the secondcross-correlation threshold and the second cross-correlation thresholdis greater than the third cross-correlation threshold; selecting forfurther consideration those sequences having the first number ofrepresentative values equal to a maximum first number of representativevalues over all sequences under consideration; selecting for furtherconsideration those sequences having the second number of representativevalues equal to a maximum second number of representative values overall sequences under consideration; removing a sequence having a largestthird number of representative values over all sequences underconsideration; removing the cross-correlation representative valuesrelated to the removed sequence; and placing remaining sequences backunder consideration.
 36. An apparatus as in claim 28, where the at leastone saved sequence comprises a plurality of saved sequences, the atleast one processor being further configured to select a subset of theplurality of saved sequences, where the at least one processor selectingthe subset of the plurality of saved sequences comprises the at leastone processor: calculating cross-correlations for each pair of sequencesof the plurality of saved sequences for a first plurality of differentcyclic shift combinations; selecting a cross-correlation value having alargest amplitude as a cross-correlation representative value for thecross-correlations between the corresponding pair of sequences; for eachpair of sequences, calculating mean squared difference between thecross-correlations and m/sqrt(N) over a second plurality of differentcyclic shift combination, where m comprises a scaling factor and Ncomprises a sequence length; iterating the sequences of the plurality ofsaved sequences in the following manner to obtain the subset of theplurality of saved sequences, where zero or more of the sequences of theplurality of saved sequences are removed on each iteration: for eachsequence of the plurality of saved sequences, counting a number ofrepresentative values exceeding a cross-correlation threshold; selectingfor further consideration those sequences having the number ofrepresentative values equal to a maximum number of representative valuesover all sequences under consideration; removing a sequence having alargest mean squared difference over all sequences under consideration;removing the cross-correlation representative values and the meansquared difference values related to the removed sequence; and placingremaining sequences back under consideration.
 37. An apparatus as inclaim 28, where the apparatus comprises a mobile station.
 38. Anapparatus as in claim 28, where the apparatus comprises a base station.